Add the last bit of the following to your script:

package Foo::Bar;

my $privateFunc1 = sub {
  ...
}

my $privateFunc2 = sub {
  ...
}

my $privateFunc3 = sub {
  ...
}

if (our $TESTING) {
   # Expose private functions for testing.
   *_privateFunc1 = $privateFunc1;
   *_privateFunc2 = $privateFunc2;
   *_privateFunc3 = $privateFunc3;
}
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By setting var $TESTING in your module's package to something true, you can now perform testing on your private functions.

BEGIN { $Foo::Bar::TESTING = 1; }
use Foo::Bar;

is( Foo::Bar::_privateFunc1($val), $expect, 'privateFunc1' );
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